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Acid-Base Equilibria (Pt. 5)
Weak Acid Equilibria and Ka- Calculating the pH of a Weak
Acid SolutionBy Shawn P. Shields, Ph.D.
This work is licensed by Dr. Shawn P. Shields-Maxwell under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Recall: Strong versus Weak Acids
Strong acids dissociate completely in solution.
Weak acids only partially dissociate in solution.
Recall: Weak Acid SolutionsSuppose a 1.0 M solution of HF (a weak acid) is prepared.What is the concentration of hydronium (H3O+) in solution? We canโt do this by inspection. An equilibrium between the weak acid and the products exists.
We need to find [H3O+] by calculating the equilibrium concentrations of HF, H3O+, and F-
H3O+
F
HF
Calculating the pH of a Weak Acid Solution
An equilibrium exists between the weak acid and its products.
We can use the relationship between the value of the equilibrium constant K and the initial concentration of weak acid in solution. HOW?
The Equilibrium Constant Ka for Weak Acids
An equilibrium exists between the weak acid (HA) and its products.
conjugate base
weak acid
The equilibrium constant K is โrenamedโ for acids to Ka
The Equilibrium Constant Ka for Weak Acids
An equilibrium exists between the weak acid (HA) and its products.
๐ ๐=ยฟยฟ Recall heterogeneous equilibriaโฆ the activity for pure liquids and solids is โ1โ
Example: The Equilibrium Constant Ka for HF
Ka is called the โacid dissociation constant.โThe value of Ka for HF is 3.5 10-4
๐ ๐=ยฟยฟ
ICE Tables, Ka, and Calculating pH for a Weak Acid Solution
Use Ka and an ICE table to determine the [H3O+] at equilibrium.
Calculate the pH using the equilibrium [H3O+]
๐ ๐=ยฟยฟ
A 0.25 M HNO2 solution is prepared.
The Ka for HNO2 is 4.6 10-4.
Calculate the pH of this solution.
Example Problem: Calculate the pH of a Weak Acid Solution
A 0.25 M HNO2 solution is prepared. The Ka for HNO2 is 4.6 10-4. Calculate the pH of this solution.
The first stepโฆ Write the chemical equation for the weak acid equilibrium.
Example Problem: Calculate the pH of a Weak Acid Solution
๐๐๐๐ (๐๐ช )+๐๐๐ (๐ฅ )โ๐๐๐+ยฟ (๐๐ช )+๐๐๐โ (๐๐ช ) ยฟ
A 0.25 M HNO2 solution is prepared. The Ka for HNO2 is 4.6 10-4. Calculate the pH of this solution.
ICE
Example Problem: Calculate the pH of a Weak Acid Solution
๐๐๐๐ (๐๐ช )+๐๐๐ (๐ฅ )โ๐๐๐+ยฟ (๐๐ช )+๐๐๐โ (๐๐ช ) ยฟ
A 0.25 M HNO2 solution is prepared. The Ka for HNO2 is 4.6 10-4. Calculate the pH of this solution.
Example Problem: Calculate the pH of a Weak Acid Solution
ICE
0.25 0 0๐๐๐๐ (๐๐ช )+๐๐๐ (๐ฅ )โ๐๐๐+ยฟ (๐๐ช )+๐๐๐โ (๐๐ช ) ยฟ
A 0.25 M HNO2 solution is prepared. The Ka for HNO2 is 4.6 10-4. Calculate the pH of this solution.
Example Problem: Calculate the pH of a Weak Acid Solution
ICE
+ x
0 00.25 x +
x
๐๐๐๐ (๐๐ช )+๐๐๐ (๐ฅ )โ๐๐๐+ยฟ (๐๐ช )+๐๐๐โ (๐๐ช ) ยฟ
A 0.25 M HNO2 solution is prepared. The Ka for HNO2 is 4.6 10-4. Calculate the pH of this solution.
Example Problem: Calculate the pH of a Weak Acid Solution
ICE
+ x
0 00.25 x +
x0.25 x xx
๐๐๐๐ (๐๐ช )+๐๐๐ (๐ฅ )โ๐๐๐+ยฟ (๐๐ช )+๐๐๐โ (๐๐ช ) ยฟ
A 0.25 M HNO2 solution is prepared. The Ka for HNO2 is 4.6 10-4. Calculate the pH of this solution.
Example Problem: Calculate the pH of a Weak Acid Solution
E 0.25 x xx
๐ ๐=ยฟยฟ
๐๐๐๐ (๐๐ช )+๐๐๐ (๐ฅ )โ๐๐๐+ยฟ (๐๐ช )+๐๐๐โ (๐๐ช ) ยฟ
A 0.25 M HNO2 solution is prepared. The Ka for HNO2 is 4.6 10-4. Calculate the pH of this solution.
Example Problem: Calculate the pH of a Weak Acid Solution
E 0.25 x xx
๐ .๐ร๐๐โ๐= ๐ฑ๐๐ .๐๐โ๐ฑ
๐๐๐๐ (๐๐ช )+๐๐๐ (๐ฅ )โ๐๐๐+ยฟ (๐๐ช )+๐๐๐โ (๐๐ช ) ยฟ
Solve for x
Solving for x (assuming x is negligible)
๐ .๐ร๐๐โ๐= ๐ฑ๐๐ .๐๐โ๐ฑ
Because Ka is small, x is very small. Assume x is zero to simplify the calculation.
๐ .๐ร๐๐โ๐= ๐ฑ๐๐ .๐๐โ๐=
๐ฑ๐๐ .๐๐
๐ .๐ร๐๐โ๐= ๐ฑ๐๐ .๐๐ (๐ .๐ร๐๐โ๐ )๐ .๐๐=๐ฑ๐
Solving for x (assuming x is negligible)
(๐ .๐ร๐๐โ๐ )๐ .๐๐=๐ฑ๐
๐ .๐๐ร๐๐โ๐=๐ฑ๐
(๐ .๐๐ร๐๐โ๐ )๐๐= (๐ฑ๐ )
๐๐
๐ .๐๐ร๐๐โ๐=๐ฑx is the [H3O+]
Calculate the pH of the Weak Acid Solution
A 0.25 M HNO2 solution is prepared. The Ka for HNO2 is 4.6 10-4. Calculate the pH of this solution.
pH = log [H3O+] = log [1.0710-2 ] = 1.97
0.25 1.0710-
2
= 0.2393 M
1.0710-2 M
๐๐๐๐ (๐๐ช )+๐๐๐ (๐ฅ )โ๐๐๐+ยฟ (๐๐ช )+๐๐๐โ (๐๐ช ) ยฟ
1.0710-2 M
Percent Dissociation
What percent of the weak acid is dissociated?
๐๐๐๐ (๐๐ช )+๐๐๐ (๐ฅ )โ๐๐๐+ยฟ (๐๐ช )+๐๐๐โ (๐๐ช ) ยฟ
% ๐๐ข๐ฌ๐ฌ๐จ๐๐ข๐๐ญ๐ข๐จ๐ง=๐๐จ๐ง๐๐๐ง๐ญ๐ซ๐๐ญ๐ข๐จ๐ง๐จ๐ ๐ก๐ฒ๐๐ซ๐จ๐ง๐ข๐ฎ๐ฆ๐๐จ๐ง๐๐๐ง๐ญ๐ซ๐๐ญ๐ข๐จ๐ง๐จ๐ ๐ญ๐ก๐๐ฐ๐๐๐ค ๐๐๐ข๐ ร๐๐๐
Percent Dissociation
What percent of the weak acid is dissociated?
๐๐๐๐ (๐๐ช )+๐๐๐ (๐ฅ )โ๐๐๐+ยฟ (๐๐ช )+๐๐๐โ (๐๐ช ) ยฟ
% ๐๐ข๐ฌ๐ฌ๐จ๐๐ข๐๐ญ๐ข๐จ๐ง=๐๐จ๐ง๐๐๐ง๐ญ๐ซ๐๐ญ๐ข๐จ๐ง๐จ๐ ๐ก๐ฒ๐๐ซ๐จ๐ง๐ข๐ฎ๐ฆ๐๐จ๐ง๐๐๐ง๐ญ๐ซ๐๐ญ๐ข๐จ๐ง๐จ๐ ๐ญ๐ก๐๐ฐ๐๐๐ค ๐๐๐ข๐ ร๐๐๐
% ๐๐ข๐ฌ๐ฌ๐จ๐=ยฟยฟ
Next up, Calculating the pH, Kb and Weak Base Equilibria (Pt 6)